Hermione's 6th Year Arithmancy
by WingedPanther73
Summary: The events of The Half-Blood Prince as revealed in Hermione's arithmancy notes. Warnings: The author of this story is a mathematician... writing about arithmancy... you do the math.


Title: Hermione's 6th Year Arithmancy

Author: WingedPanther73

Pairing(s)/Characters: Hermione

Rating: G

Summary: The events of _The Half-Blood Prince_ as revealed in Hermione's arithmancy notes.

Warnings: The author of this story is a mathematician... writing about arithmancy... you do the math.

Disclaimer: Harry Potter, its names and characters belong to J.K. Rowling.

Beta Reader: Sybil Rowan

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1st August, year 6.

After studying arithmancy for three years, we're finally going to be creating unique objects. Beginning arithmancy in year three was cute, at first. The numerology component was pretty easy, and more satisfying than the nonsense Trelawny's taught. It was really the only sane way to get the "fortune telling" credit. Personally, I find astrology far more useful for telling the future.

I'm so glad that I had muggle maths before coming to Hogwarts. It really helped me out that year. I had already studied most of the course as a muggle student. My parents sent me some books on long division that really helped me complete the year. Their book on fractions was essential to getting me through the last test.

Half the students dropped arithmancy as a subject when fourth year came around, and it was just as well. Using numbers to quantify things and make predictions was trickier than it seemed. Mum said she had studied something similar in a class called "statistics". She sent me a few pointers from her studies that were quite useful. When I brought this to Professor Vector's attention, she admitted that the best arithmancers have studied "mathematics" and "physics" in muggle universities. I may want to do that myself, although I want to be sure I can secure a job in the department of mysteries first.

Only a quarter of the students signed up for fifth year arithmancy. It was probably just as well. The students who made high marks in the fourth year were the only ones who made passing marks in fifth year. Professor Vector kept referring to "what muggles call 'topology'" and "what muggles call 'physics'".

Dad said he had an old chum from university who studied that stuff. It was a bunch of advanced maths and theoretical physics. The difference was, while theoretical physics talks about the concept of bending space-time, in arithmancy we studied how the levitation charm actually _was_ bending space-time. Professor Vector allowed us to watch how the "gravity waves" were redirected to provide lift and motion. She had a number of special devices for viewing the forces at work.

Every charm was studied, based on the arithmancic concepts of "temporarily redefined metrics and topologies, and their understanding as a mechanism for improving effectiveness and control in casting charms." Each charm required its own paper. When I asked Professor Flitwick for some advice on one, he said that arithmancy detracted from the art of charms, and refused to offer any advice on my papers.

I am somewhat disappointed in my final paper on the functioning of brooms. Forty pages simply wasn't enough parchment to properly address the intricacies of how they function. Ron just rolled his eyes when he saw my diagrams, the oaf. He would really have done well to study arithmancy with me, it would help him out so much in charms. Neville refused to even talk with me about it.

Professor McGonagall informed me during my counseling that an Exceeds Expectations on my arithmancy O.W.L. is required to move on and be considered for employment in the ministry of mysteries. I will also need to do well on my N.E.W.T.s for arithmancy. Now to write reviews of all my other courses before classes start tomorrow.

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16th August, year 6.

Almost finished enchanting this stupid broom. With all the work I did last year on various motive charms, you would think this would be easy. Ron saw my broom zipping around the commons last night and asked McLaggen if he'd borrowed my broom for tryouts! The problem with the broom is getting it to react to the rider's desire.

With a charm, you unconsciously direct the gravity lines to produce a graceful movement. With enchantment, you have to make the broom interpret the wishes of the rider. It's quite complicated. I tried to explain what making a broom has to do with arithmancy to Neville, but his eyes sort of glazed over. I should have the enchantments done in another hour or so.

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17th August, year 6

Got to bed at one in the morning. It was worth it, as the final enchantment made the difference between my broom being rated as a Cleansweep two or a Cleansweep three. I still think that Ron and Harry need to spend more time studying and less time on Quidditch, but I must say I appreciate the craftsmanship of their brooms a lot more.

Professor Vector introduced us to redefining metrics to increase space inside of objects. We began studying a typical wizards tent and comparing it with a muggle tent. While both tents were the same size on the outside, the wizards tent was much larger inside. To help us understand what was happening, Professor Vector pulled out some speciallized lenses that are enchanted to reveal distortions of regular space. When we viewed the entrance to the wizards tent, we could clearly see how the metric, or measure of distance, changed at the entrance of the tent to make the interior larger than it should have been.

Homework for tonight is ten pages on the theory of metrics as applied to spacial distortion in tent-making, with special attention to techniques for preventing disorientation at boundaries. Extra marks for correctly explaining the arithmancic equations that are required.

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20th August, year 6

Because of the amount of details, Professor Vector is requiring us to work in a group to enchant the muggle tent. I don't mind working with Lisa Turpin, but Anthony Goldstein keeps trying to flirt with me, and it's quite annoying! He even had the audacity to ask if I'd snogged Krum, as if it was any of his business!

We have two weeks to modify the tent to allow it to comfortably hold twelve people. Special care must be made to avoid inducing queasiness in any part of the tent and also ensure that the outside of the tent is not affected or compromised in any way. Lisa and Anthony have left me in charge of the calculations while they cast the spells to adjust the metrics.

For some reason, Lisa is particularly prone to getting queasy when different parts of her suddenly change relative distances. As a result, we're planning to have Lisa test for queasiness on a daily basis. Professor Vector has given us permission to work on the tent in the classroom, since we're from different houses.

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7th October, year 6

We got extra marks for the quality of our stairs, but Professor Vector found where Anthony and put a recliner in front of a nausea spotted corner that I didn't have time to rework the equations on. Lisa spent a little too much time decorating, though I think that Anthony and her were snogging in one of the side rooms inside the tent while I was trying to work out how to sharpen the corners for the steps.

Overall, we got high marks and Anthony has stopped pestering me. We now have four more weeks to modify the tent so it can be folded up without damaging the contents. On a side note, Harry's been acting sort of weird lately. He's got a lot of really paranoid theories about Malfoy. I offered to show him some of what I've been studying, but he huffed off. Malfoy's always up to something, but he really shouldn't worry so.

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14th October, year 6

The past weekend has been so hectic, I completely forgot to work on making the tent collapsible! Between Harry casting that stupid _Levicorpus_ spell and Katie Bell landing in the infirmary, things have gotten a bit scary. Harry's convinced that Draco's involved, but that's just silly. I hope his lesson goes well tonight. I'm thinking about inviting Ron to the Christmas party for the Slug Club, but I don't know if he'll agree.

Bollucks, I let my concentration slip again. Getting the formulas right so we can fold up the tent is trickier than we first thought. Our original design is causing the tent flaps to stick, and the chandelier keeps bashing into the floor whenever we lower the top pole. All three of us are working like crazy to figure out how to accommodate the tent folding. I just wish they'd stop going all googly eyed at each other all the time. We're going to have to spend at least an hour every evening on this if we want to stand any chance of getting this to work in time!

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16th October, year 6

Good news! Ron'll go with me! Oh yeah, and I figured out the key to getting the tent to collapse without making a mess of everything. It's a combination of flexible metrics near the entrance, and also being careful to enforce the gravity vectors as the orientation changes. I think that we can get all to formulas figured out by the end of the week and spend next week implementing the changes. It'll be tight, but we should make it.

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28th October, year 6

We just managed to finish all the changes. We even fixed the squeamish corner. Looking back on it, our initial set of formulas was just garbage. We had the metrics all wrong for a collapsible tent, but the new set are working beautifully. Our final test was to have me collapse the tent while Lisa and Anthony were snogging inside. I think they got a little to into the snogging and not enough into the fact that we were conducting a test, because I had to turn my back when I went back in after setting up the tent again. I'm not sure anything would have distracted them.

Professor Vector was very pleased with our results and gave us full marks. I've been reading ahead and it looks like we're going to have several weeks of theory as we discuss the Floo Network and portkeys in detail. In particular, it looks like casting _Portus_ will be trickier than I had hoped.

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4th November, year 6

[note: the following notes are not representative of Hermione's usual handwriting, even allowing for the tear stains on the page] That horrible, insufferable lout! I invite him to the Christmas party, and he goes and snogs HER! [blotchs of ink and water stain] cold shoulder for a week and then this. I've never been so humiliated in my life! [continued blotches] Harry says Mrs. Pomfrey patched him up in no time. I should have been summoning goshawks instead of finches.

Dammit! Why won't these Floo formulas work out?

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11th November, year 6

Dealing with fourth dimensional equations is becoming a little tiresome. These "wormholes" that the Floo Network is made of seem to be a stable realization of some muggle ideas. Apparently it's some sort of chain of fourth dimensional tubes, with the Floo Powder acting as a control as you bounce through successive tubes.

Portkeys operate under the same principle, but aren't as stable. Apparently the entire network of Floo and portkey tubes requires a lot of care to avoid problems with them colliding with each other. The formulas are a bit tricky.

Ron's an idiot.

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25th November, year 6

We've created a miniature version of the Floo Network for mice to travel through. It has five points to it, but actually keeping the tubes stable has been a challenge. They keep wanting to collapse, and two of them keep getting tangled. The mice seem to have adjusted to the odd mode of travel, and can be seen hopping in and out of Floo points to move from the water chamber to the food chamber.

I figure if I go to the Christmas party with McLaggen, maybe that will get Ron's attention away from Lavender. What does he see in her anyway?

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16th December, year 6

We've successfully created Portkeys for traveling across the room. The first few kept tangling with the mouse Floo Network, but we finally figured out how to nudge the Floo Network "up" and the portkeys "down" so that they wouldn't collide. The rest of this week will be practical tests on creating temporary and stable fourth dimensional tubes, and how to protect them from disruption.

McLaggen agreed to go with me, but he's a complete idiot. No better than Ron, really.

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6th January, year 6

Harry is positively obsessed with the idea that Snape is a traitor to the Order. I don't believe him, but it does seem suspicious. The evidence that Malfoy's up to something is a bit more concrete, though. Harry's obsessed with the idea that Draco will get someone in here, but it's just not possible. I don't quite have the details figured out, but interrupting the tubes into Hogwarts shouldn't be that hard to do. I just haven't figured out how the Floo Network would work but apparating wouldn't... they seem to work on the same principle.

Speaking of apparating, we'll be studying that for the next few weeks in arithmancy class. It seems that apparition works on the same principle as portkeys. There are some key differences, but our studies should help make apparition lessons and passing the apparition test much easier. The goal is to make sure we can all get licensed on our first try. Professor Vector indicated that the results of our apparition test will figure heavily into our grade this year.

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3rd February, year 6

After all of the study on apparition, you'd think I could have made some progress! At least "Won-Won" didn't get more than a tingle in his trainers. Still, I know the formulas! There's something about making that push through a fourth dimensional pinch that isn't the same as creating a tube at all!

Maybe I distracted myself, I don't know. Destination, Determination, Deliberation. What does that have to do with the process of creating a fourth dimensional fold to slide through? I do feel sorry for Susan letting the pinch close around her leg, though.

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3rd March, year 6

At least I haven't splinched myself! I can feel the pressure, I can sense how close I am to breaking through. Lisa and Anthony are having the same frustration as I am, we should have been able to punch through by now, and we can't practice during arithmancy because of the anti-apparition spell over Hogwarts.

Fourth dimensional folds just aren't possible in the castle! To make matters worse, Ron got himself poisoned after taking a stupid love potion. The only good part is that Lavender seems pretty upset.

Professor Vector has assigned us our final project for the year. We are to each craft a single object that makes use of the concepts we have studied this year. I've got an idea, but I need to work out the details.

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17th March, year 6

Ron said he loves me! I don't know if he really means it or just loves my spell checking, but Lavender will be out of the picture soon.

Professor Vector approved my preliminary design. The calculations are going to be pretty rough. I need to adjust the gravity vectors while distorting the space inside. My initial model is based off the purse of Fortunatus, but I think I can come up with something a little more practical.

At least people are so used to seeing me knitting socks for the house elves that they won't pay too much attention to me knitting with my wand. As a bonus, I think I'm getting the hand of apparating. Professor Vector was right when she said that all the arithmancy in the world won't make up for a little intuition and boldness.

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31st March, year 6

My purse should work nicely. The calculations will definitely have to be woven into every strand to enable it to work properly. I learned my lessons from the tent fiasco. The last thing I want is a purse that can't adjust its shape naturally, or one that will toss things around inside. I want to be able to hold at least fifty books, plus supplies. It will make getting around next year so much easier when I can just stroll from class to class instead of struggling with my books.

The apparition testing is in three weeks, and I'm confident that I'm ready for it. The key was to relax. The formulas are helpful, but the courage to push the pinch open and slip through is the true key. I had forgotten that a spell is not an enchantment, and understanding what the magic does is not the same as casting the spell. I think Professor Flitwick was partially right. I wish I had realized it at the time.

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22nd April, year 6

Ron finally blew off Lavender and I passed the apparition test! Harry got the memory as well! Professor Vector just approved my design. It'll take the rest of the year for me to actually make the purse.

I took my inspiration from the purse of Fortunatus, as it makes increasing the capacity of the purse easier with the four dimensional twist. I still do some work on adjusting metrics and redirecting gravity fields, but the whole design is much more stable this way.

I considered asking Ron if I could borrow his wand as a second knitting needle, but I think I'll be better off just using my own wand and a standard one. I'll need a lot of time to finish this, and the concentration to maintain the necessary spells and knit them into the purse will be terrible. This is going to make polyjuice potion look like a casual construct.

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12th May, year 6

Harry got himself in permanent detention. I _knew_ that book was trouble! I'm amazed he wasn't expelled! At least Ron was able to lead Gryffindor to victory in the quidditch cup. Since Harry kissed Ginny, they've been almost inseparable. I wish Ron would get the courage to kiss me.

I've got the purse started, but it's devilishly tricky. It seems like every three loops I have to undo two and rework them. The yarn's as important as the spellwork, I've found. I actually snuck out to Hagrid's and dug up a corner of Aragog's grave so I could gets some of his hairs for my yarn. For some reason, that's made the whole process a lot easier.

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26th May, year 6

The purse is nearly completed. Using hairs from Aragog has really helped me out. I should be done by the end of the week.

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3rd June, year 6

I completed my purse and Professor Vector already graded it! I got extra marks for the creative use of loops to reinforce the internal structure while cushioning the motion of the purse. Having most of the contents in a fourth dimensional pouch that uses artificially directive gravity fields helped as well. Overall, I'm very pleased. Anthony looks upset about Lisa getting higher marks on her project than he did. Trust a boy to think building a better knarl trap is a worthwhile demonstration of spatial distortion magic.

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4th June, year 6 [last entry]

It's horrible! Dumbledore's dead. I can't believe I didn't realize it! Of course a fourth dimensional tube can get past the defenses. The Floo Network is guarded, but if someone had created a stable alternative, it would work. If only I'd gone with Harry to figure out what was going on, Dumbledore would still be alive and there wouldn't have been death eaters all over the castle last night.

The worst thing is that Snape betrayed us all! The Order isn't safe at headquarters, either. This is a disaster! Everything's ruined.

I have to go to the funeral now. Hopefully we can figure something out.


End file.
